This disclosure is related to the following simultaneously-filed disclosures that are incorporated herein by reference:
Coherent Population Trapping-Based Method for Generating a Frequency Standard Having a Reduced Magnitude of Total a.c. Stark Shift of inventors Miao Zhu and Leonard S. Cutler; Ser. No. 09/588,045,
Coherent Population Trapping-Based Frequency Standard Having a Reduced Magnitude of Total a.c. Stark Shift of inventors Miao Zhu and Leonard S. Cutler 09/587,719; and
Detection Method and Detector for Generating a Detection Signal that Quantifies a Resonant Interaction Between a Quantum Absorber and Incident Electro-Magnetic Radiation of inventors Leonard S. Cutler and Miao Zhu Ser. No. 09/588,032.
The invention relates to high-precision frequency standards and, in particular, to atomic frequency standards based on coherent population trapping (CPT).
The proliferation of telecommunications based on optical fibers and other high-speed links that employ very high modulation frequencies has led to an increased demand for highly-precise and stable local frequency standards capable of operating outside the standards laboratory. Quartz crystals are the most commonly-used local frequency standard, but in many cases are not sufficiently stable to meet the stability requirements of modern, high-speed communications applications and other similar applications.
To achieve the stability currently required, a frequency standard requires a frequency reference that is substantially independent of external factors such as temperature and magnetic field strength. Also required is a way to couple the frequency reference to an electrical signal that serves as the electrical output of the frequency standard. Potential frequency references include transitions between quantum states in atoms, ions and molecules. However, many such transitions correspond to optical frequencies, which makes the transition difficult to couple to an electrical signal.
Transitions between the levels of certain ions and molecules and between the hyperfine levels of certain atoms have energies that correspond to microwave frequencies in the 1 GHz to 45 GHz range. Electrical signals in this frequency range can be generated, amplified, filtered, detected and otherwise processed using conventional semiconductor circuits.
An early example of a portable frequency standard based on an atomic frequency reference is the model 5060A frequency standard introduced by the Hewlett-Packard Company in 1964. This frequency standard used a transition between two hyperfine levels of the cesium-133 atom as its frequency reference, and had a frequency accuracy of about two parts in 1011. Current versions of this frequency standard have an accuracy of about five parts in 1013 and a stability of a few parts in 1014.
Less accurate but smaller frequency standards have been built that use a transition between the hyperfine states of a suitable quantum absorber as their frequency reference. The quantum absorber is confined in a cell located in a microwave cavity. FIG. 1 is an energy diagram of a simplified quantum absorber. The quantum absorber has a ground state that is split into two groups of sub-states by the hyperfine interaction. At room temperature, all the sub-states in the two groups are approximately equally populated. For convenience, the two groups of sub-states into which the ground state S of the quantum absorber is split by hyperfine interaction will be called the lower ground state |g1 greater than  and the upper ground state |g2 greater than . The upper ground state and the lower ground state are separated by an energy corresponding to an angular frequency xcfx890 in the microwave frequency range. References in this disclosure to frequency should be taken to denote angular frequency.
The quantum absorber additionally has an excited state |e) that is also split by hyperfine interaction into groups of sub-states. The energy differences between the groups into which the excited state is split are small, so the excited state will be treated as a single state in this discussion. The excited state is essentially unpopulated at room temperature.
The quantum absorber is illuminated with monochromatic light having a frequency that corresponds to the energy of the transition between one of the ground states and the excited state. The monochromatic light is conventionally generated by a lamp whose output is filtered to remove all but the desired frequency. For example, consider the transition between the lower ground state |g1 greater than  and the excited state |e greater than . These states have energies of Eg0 and Ee0, respectively. The transition frequency xcfx891 corresponding to the energy of this transition is:
xcfx891=(Eg0xe2x88x92Ee0)/h,
where h is Planck""s constant divided by 2xcfx80.
When the monochromatic light has a frequency xcfx891, the quantum absorber can absorb a quantum of the light, which causes the quantum absorber to move from the lower ground state |g1 greater than  to the excited state |e greater than . The quantum absorber shown can return from the excited state to either one of the ground states, emitting a quantum of fluorescent light. When the quantum absorber returns to the lower ground state, the monochromatic light can move it back to the excited state. However, when the quantum absorber returns to the upper ground state |g2 greater than , the monochromatic light is incapable of moving it back to the excited state. Thus, after one or more absorption/emission cycles, absorption of the incident light and emission of fluorescent light cease because the quantum absorber becomes trapped in the upper ground state. Thus, the monochromatic light creates a population imbalance between the ground states.
Feeding microwave energy into the microwave cavity at a frequency corresponding to the energy difference between the two ground states tends to equalize the populations of the ground states. The change of population causes the absorption of the light transmitted through the cell to increase. The increase can be detected and the resulting detection signal can be used to control the microwave frequency to a frequency at which the absorption of the light transmitted through the quantum absorber is a maximum. When this condition is met, the microwave frequency corresponds to, and is determined by, the energy difference between the ground states. The microwave signal, or a signal derived from the microwave signal, is used as the frequency standard.
The energy difference between the ground states is relatively insensitive to external influences such as electric field strength, magnetic field strength, temperature, etc., and corresponds to a frequency that can be handled relatively conveniently by electronic circuits. This makes the energy difference between the ground states a relatively ideal frequency reference for use in a frequency standard.
More recently, frequency standards have been proposed that use as their frequency reference coherent population trapping (CPT) in the ground states of a quantum absorber. For example, a CPT-based frequency standard is described by Normand Cyr, Michel Txc3xaatu and Marc Breton in All-Optical Microwave Frequency Standard: a Proposal, 42 IEEE TRANS. ON INSTRUMENTATION and MEASUREMENT, 640 (April 1993). The structure of a CPT-based frequency standard can be similar to that of the frequency standard described above, but the CPT-based frequency standard uses a semiconductor laser as its light source, and only includes a microwave cavity if coherent emission, to be described below, is detected. The quantum absorber is illuminated with incident light having two main frequency components. Each of the main frequency components has a frequency that corresponds to the energy of the transition between one of the ground states |g1 greater than  and |g2 greater than  and the excited state |e greater than  of the quantum absorber. The incident light can be generated using two phase-locked lasers or by modulating the frequency of a single laser. In the former case, the frequency difference between the main frequency components is determined by the frequency difference between the lasers. In the latter case, the frequency difference between the main frequency components is determined by the modulation frequency applied to the laser.
Illuminating the quantum absorber with incident light containing only one main frequency component having a frequency xcexa91 corresponding to the energy of the transition between the lower ground state |g1 greater than  and the excited state |e greater than  would result in the absorption of the incident light and the emission of the fluorescent light ceasing after the quantum absorber became trapped in the upper ground state |g2 greater than , as described above. Similarly, illuminating the quantum absorber with incident light containing only one main frequency component having a frequency xcexa92 corresponding to the energy of the transition between the upper ground state |g2 greater than  and the excited state |e greater than  would result in the absorption of the incident light and the emission of the fluorescent light ceasing after the quantum absorber became trapped in the lower ground state |g1 greater than .
Illuminating the quantum absorber with incident light containing both main frequency components whose frequencies xcexa91 and xcexa92 correspond to the energy differences between the lower ground state and the upper ground state, respectively, and the excited state establishes a specific coherence between the ground states, i.e., a condition in which the quantum absorber is in a specific superposition of the ground states. The quantum absorber in this specific superposition of the ground states does not interact with the two main frequency components of the incident light. This leads to the name dark state, or coherent population trapping (CPT) state for the superposition of the ground states. When the quantum absorber is composed of multiple quantum absorber elements, such as multiple atoms, absorption of the incident light by the quantum absorber is minimized when the number of quantum absorber elements in the CPT state reaches a maximum. In this condition, transmission of the incident light through the quantum absorber is maximized and emission of fluorescent light by the quantum absorber is minimized.
The quantum absorber in the CPT state has an oscillating electromagnetic multipole moment at a frequency equal to the frequency difference. The oscillating electromagnetic multipole moment emits an electromagnetic field called coherent emission. When the number of quantum absorber elements in the CPT state reaches a maximum, the coherent emission generated by the quantum absorber is maximized.
Generation of the CPT state is detected by detecting the electromagnetic radiation from the quantum absorber. The electromagnetic radiation from the quantum absorber is any one of the portion of the incident light that remains unabsorbed after passing through the quantum absorber, the fluorescent light generated by the quantum absorber in response to the incident light and the coherent emission generated by the quantum absorber in response to the incident light. The resulting detection signal is fed to a servo system that controls the frequency difference between the main frequency components to one at which the unabsorbed portion of the incident light has a maximum intensity, the fluorescent light generated by the quantum absorber has a minimum intensity or the coherent emission generated by the quantum absorber has a maximum intensity. When the number of quantum absorber elements in the CPT state reaches a maximum, the frequency difference between the main frequency components corresponds to, and is determined by, the energy difference between the ground states.
The accuracy and stability of the frequency standard depends on the precision with which the maximum or the minimum (collectively, the extremum) in the detection signal can be determined. The extremum in the detection signal indicates the corresponding extremum in the intensity of the corresponding one of the unabsorbed portion of the incident light, the fluorescent light and the coherent emission that occurs when the frequency difference between the main frequency components corresponds to the energy difference between the ground states.
The CPT-based frequency standards that have been reported in the literature generate the CPT state using quantum absorber transitions that generate the CPT state with low efficiency. A quantum absorber transition is a specific transition of a specific quantum absorber, for example, the D2 line of rubidium-87 atoms. Generating the CPT state with low efficiency impairs the stability and accuracy of the frequency standards by two main mechanisms. First, the intensity of the electromagnetic radiation from the quantum absorber at the extremum differs from the background level of the electro-magnetic radiation by from about 0.3% to about 1%. The background radiation contributes noise to the detection signal, which reduces the stability with which the small change in the detection signal representing the extremum is detected. This impairs the stability of the frequency standard.
Second, generating the CPT state with low efficiency requires the incident light that illuminates the quantum absorber to have a high intensity to counteract the effects of a relaxation process that removes quantum absorbers from the CPT state. The incident light subjects the quantum absorber to an a.c. Stark shift that changes the energy levels of the ground states of the quantum absorber and, hence, the frequency corresponding to the energy difference between these states. The a.c. Stark shift depends on the intensity of the incident light, so high intensity incident light subjects the energy levels to a large a.c. Stark shift, which impairs the accuracy of the frequency standard. Moreover, variations in the intensity of the incident light cause variations in the a.c. Stark shift, and variations in the energy difference between the ground states, which degrade the stability of the frequency standard.
Frequency standards having an increased accuracy and stability are required to meet the requirements of modern, high-speed communications and other applications. Thus, what is needed is a CPT-based method for generating a frequency standard that generates the CPT state with higher efficiency to improve in the accuracy and stability of the frequency standard.
The invention provides a method for generating a frequency standard. In the method, a quantum absorber having a transition between a lower quantum state and an upper quantum state is provided. The lower quantum state is split by hyperfine interaction into two lower sub-state groups of at least one lower sub-state. The upper quantum state is split by hyperfine interaction into upper sub-state groups of at least one upper sub-state. None of the upper sub-state groups is a cycling transition sub-state group that has at least one allowed electric dipole transition to one of the lower sub-state groups but no allowed electric dipole transitions to the other of the lower sub-state groups. The upper quantum state differs in energy from a first lower sub-state in one of the lower sub-state groups and from a second lower sub-state in the other of the lower sub-state groups by energy differences that correspond to transition frequencies of xcfx891 and xcfx892, respectively. Incident electromagnetic radiation including two main frequency components that have frequencies respectively equal to xcfx891 and xcfx892 is generated. The main frequency components differ in frequency by a frequency difference. The quantum absorber is irradiated with the incident electromagnetic radiation. Electro-magnetic radiation from the quantum absorber is detected to generate a detection signal. The frequency difference is controlled to obtain an extremum in the detection signal. The extremum indicates that the frequency difference corresponds to the energy difference between the first lower sub-state and the second lower sub-state. A frequency standard signal related in frequency to the frequency difference is then provided.
The invention also provides a frequency standard that comprises a quantum absorber, a source of incident electromagnetic radiation, a detector, a frequency difference controller and a frequency standard signal output. The quantum absorber has a transition between a lower quantum state and an upper quantum state. The lower quantum state is split by hyperfine interaction into two lower sub-state groups of at least one lower sub-state. The upper quantum state is split by hyperfine interaction into upper sub-state groups of at least one upper sub-state. None of the upper sub-state groups is a cycling transition sub-state group that has at least one allowed electric dipole transition to one of the lower sub-state groups but no allowed electric dipole transitions to the other of the lower sub-state groups. The upper quantum state differs in energy from a first lower sub-state in one of the lower sub-state groups and from a second lower sub-state in the other of the lower sub-state groups by energy differences that correspond to transition frequencies of xcfx891 and xcfx892, respectively. The source of incident electromagnetic radiation is arranged to irradiate the quantum absorber. The incident electromagnetic radiation includes two main frequency components that have frequencies respectively equal to xcfx891 and xcfx892. The detector is arranged to receive electromagnetic radiation from the quantum absorber and generating a detection signal in response to the received electromagnetic radiation. The frequency difference controller operates in response to the detection signal to control the source to generate the main frequency components with a difference in frequency that obtains an extremum in the detection signal. The extremum indicates that the difference in frequency corresponds to an energy difference between the first lower sub-state and the second lower sub-state. The frequency standard signal output provides a frequency standard signal related in frequency to the difference in frequency.
The frequency standard generating method and frequency standard of the invention employ a quantum absorber transition whose upper quantum state has no cycling transition sub-state groups, i.e., sub-state groups that have at least one allowed electric dipole transition to one of the lower sub-state groups but no allowed electric dipole transitions to the other of the lower sub-state groups. Cycling transition sub-state groups in the upper quantum state of a quantum absorber significantly reduce the efficiency with which the CPT state is generated. A quantum absorber transition whose upper quantum state has no cycling transition sub-state groups generates the CPT state with a substantially increased efficiency. Using such a quantum absorber transition in a CPT-based frequency standard increases the accuracy and stability of the CPT-based frequency standard.